Question

If $x,y,z$ are real numbers satisfying the equations $x+\left[y\right]+\left\{z\right\}=12.00,\left[x\right]+\left\{y\right\}+z=13.54,\left\{x\right\}+y+\left[z\right]=14.70,$ where [.] & {.} represents greatest integer function & fractional part respectively,
then

• A. $x+y+z=20.12$
• B. $(x+z)$ is an integer
• C. $\left[y\right]+\left\{x\right\}+\left\{z\right\}=7$
• D. $(\left[x\right]+\left[y\right]+\left[z\right])$ is an odd integer.

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $x+y+z=20.12$
B $(x+z)$ is an integer
C $\left[y\right]+\left\{x\right\}+\left\{z\right\}=7$
D $(\left[x\right]+\left[y\right]+\left[z\right])$ is an odd integer.